Re: How is the degree of membership calculated?

Hartwig Jeschke (jeschke@mst.uni-hannover.de)
Tue, 28 Apr 1998 17:50:56 +0200 (MET DST)

CRPFALKSD wrote:

> Question: How is the degree of membership calculated?

Please find enclosed, how I have implemented the membership function, wherea fuzzy
interval is characterized by a set of parameters [m1, m2, a, b] with an trapezoidal

shape:

m1- a : mu = 0
m1 : mu =1
m2 : mu =1
m2+b: mu =0

Your Example "Just Right" would be [65, 65,5, 5].

function MemberShip(X: Real): FuzzyInterval;
Begin
Result := 0.0;

if (x > A.m1-A.a) and (x < A.m1) then

Result := (x - A.m1 + A.a)/ A.a;

if (x >= A.m1) and (x <= A.m2) then

Result := 1.0 ;

if (x > A.m2) and (x < A.m2 +A.b) then

Result := 1.0 + (A.m2 - x) / A.b;
End;

Using this approach and if I am right with it, the result for your point "O" is
0.6 of "Just Right" and not (!!!) 0.8.

You can test the function using my free Win95 program FzCalc 1.1 "X in Y" Function,

which is available in the Download-Area of:

http://www.mst.uni-hannover.de/~vspdecis

Additionally my program can evaluate the degree of membership of a fuzzy interval
within an
another fuzzy interval, too. - Which is much more complex, when compared to your
real-valued
input.

I hope, that I could help you

Hartwig Jeschke